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Apr
29
accepted Embedding abelian cancellative Hausdorff topological semigroups into abelian Hausdorff topological groups
Apr
9
accepted Generalizations and relative applications of Fekete's subadditive lemma
Apr
8
comment Are the extremal points of a certain set of functions $\mathcal P(\mathbf N) \to \bf R$ weakly additive?
Right, right. One question that comes to mind could be: Which of the "classical upper densities" is extremal (in $\mathscr U$)? For instance, is the upper logarithmic density extremal?
Apr
8
comment Are the extremal points of a certain set of functions $\mathcal P(\mathbf N) \to \bf R$ weakly additive?
To me, it looks correct (and nice). In addition, it has the merit of showing that every upper [quasi-]density is a convex combination of extremal upper [quasi-]densities, which could motivate some other questions.
Apr
8
comment Are the extremal points of a certain set of functions $\mathcal P(\mathbf N) \to \bf R$ weakly additive?
A minor detail: I think you mean "weakly additive upper density" wherever your write "weakly additive measure", don't you?
Apr
8
accepted Are the extremal points of a certain set of functions $\mathcal P(\mathbf N) \to \bf R$ weakly additive?
Mar
22
awarded  Nice Question
Mar
14
comment Embedding a cancellative monoid into another in such a way that $|X-x|=|X|$, where $X$ is a fixed finite set and $x\in X$
Sorry for the delay, I was in a hurry this afternoon and didn't realize that there were at least three things I had to fix in the old formulation. In particular, I would/should have asked if $\mathbb B$ can be embedded into $\mathbb A$ in such a way that at least one $x\in X$ becomes right-subtractive. @BenjaminSteinberg. Yes, and if $\mathbb A$ is a canc. monoid, then the right-subtractive elements of a finite set $X$ that contains the identity of $\mathbb A$ are precisely the left-invertible elements of $\mathbb A$ (hence $X^{\rm rs}=\mathbb A^\times$, from what you made me note yesterday).
Mar
14
revised Embedding a cancellative monoid into another in such a way that $|X-x|=|X|$, where $X$ is a fixed finite set and $x\in X$
Changed a word in the title
Mar
14
revised Embedding a cancellative monoid into another in such a way that $|X-x|=|X|$, where $X$ is a fixed finite set and $x\in X$
Fixed a couple of issues in the formulation of the question
Mar
14
revised Embedding a cancellative monoid into another in such a way that $|X-x|=|X|$, where $X$ is a fixed finite set and $x\in X$
added 10 characters in body
Mar
14
asked Embedding a cancellative monoid into another in such a way that $|X-x|=|X|$, where $X$ is a fixed finite set and $x\in X$
Mar
14
revised Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible
Removed some text that was no longer meaningful (after Benjamin Steinberg's remark)
Mar
13
accepted Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible
Mar
13
revised Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible
Embedded BS's remark
Mar
13
comment Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible
To my shame, I hadn't thought of it. Let me edit and include your remark.
Mar
13
asked Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible
Mar
6
comment Numerical and topological density
@Dominic. I jumped to hasty conclusions. I take my comment back, and agree that $F$ is a filter. On the other hand, what's the meaning of the superscript '+' appended to a subfamily of $\mathcal P(\mathbf N)$?
Feb
23
comment Density of ratios of an arbitrary increasing sequence of prime numbers
For the record, I've just learned of an erratum to the paper of Strauch and Tóth I mentioned above, namely: O. Strauch and J. T. Tóth, Corrigendum to Theorem 5 of the paper “Asymptotic density of $A\subseteq \mathbb N$ and density of the ratio set $R(A)$ (Acta Arith. 87 (1998), 67--78), Acta Arith. 103 (2002), No. 2, 169-189 (impan.pl/en/publishing-house/journals-and-series/…).
Feb
14
revised How to cite authors from any country correctly?
deleted 5 characters in body